Optical identifications have been sought for 198 southern radio sources (73 in Paper I, 06h<RA(B1950)<18h and 125 in Paper II, 18h<RA(B1950)<06h) using new positions determined with the six-dish array of the Fleurs synthesis telescope. These sources constitute a complete sample drawn from the Parkes 2700-MHz catalogue. They are all flat-spectrum sources stronger than 0.25 Jy at 2700 MHz and lie between Dec(B1950) -80 and -50{deg}. Sources with |b|<5{deg} are not included. The new radio positions have standard deviations of about 1'' (2'' in Paper I, 1'' in Paper II) in right ascension and declination. The optical positions are with respect to the FK4 reference system as defined by the Perth catalogues and have position uncertainties of about 0.5arcsec. Magnitude estimates are on the J scale and are accurate to about 0.4mag for stellar-like objects and 0.5 to 1.0mag for galaxies. The sample is complete to the 22.5-mag limit of the SERC-J sky atlas. There are 198 sources in the complete sample. 31 sources (16%) show some radio structure with the 2'' beam. For the 175 unresolved sources, there are 124 QSOs (71%), 26 galaxies (15%) and 25 empty fields (14%) suggested.